Fluid Mechanics for Civil EngineeringReviewPrimary Dimensions & Units Dimension: Generalization of unit telling us what kind of units are involved in a quantitative statement Mass [M], length [L], time [T], temperature [] Mass [M], length [L], time [T], temperature [] Unit: Particular dimension kg, m, s, oK (Systeme International) slug, ft, s, oR (British Gravitational) lbm, ft, s, oR (something else)Secondary Units ForceN= kg-m/s2(Newton)lbf= slug-ft/s2(pound force)= 32.2 lbm-ft/s2 Work (Force through a distance)| |((

=((

=2 2TLMTMLma Frr Work (Force through a distance)J = N-m (Joule)ft-lbf (foot pound) Energy (Work per time)W = J/s (Watt)ft-lbf/s (foot pound per sec)hp 550 ft-lb/s (horsepower)Table A.4APPROXIMATE PHYSICAL PROPERTIES OF COMMON LIQUIDS AT ATMOSPHERIC PRESSURETable A.2PHYSICAL PROPERTIES OF GASES AT STANDARD ATMOSPHERIC PRESSURE AND 15C (59F)Pressure Fluid at rest can not support shear stress Normal stress on any plane is pressure (+ for compression) compression)p p p p pp py l l l y p l y p Fp p l y p l y p Fz y x nz nn z zx n n x x= = = = = = == = = sin cos21cos cos 0sin sin 0Pressure, Absolute & GagePressure Variation with Elevation Static fluid pressure varies only with elevation in the fluid.0F F FFl == sin ) ( l A A p p A pF F Fweight right left + = =dldzdldplzlp = = =or sin =dzdpPressure on Plane Surface sin y p =dAxFSurfaces exposed to fluids experience a force due to the pressure distribution in the fluidyycpyCentroidCenter of pressureA p FA y FydAdA ypdA FAAA=====) sin (sinsin Line of Action of Force Lies below centroid, since pressure increases with depthydF F ycp= sin y p =dAxyycpyCentroidCenter of pressureFA yIy yA y I A y yI A y ydA y ypdA ycpcpcpAAcp+ =+ ====20) (sin ) sin () sin () ( Pressure on Curved Surfacex ACx ACxF FF FF= ==0FxycpFyCB yCB yyF W FW F FF+ = ==0Archimedes Principle Archimedes PrincipleFB= weight displaced fluid Line of action passes through the centroid of displaced volumeFluid Motion Two ways to describe fluid motion Lagrangian Follow particles aroundk j i Vdtdzdtdydtdx+ + = Follow particles around Eulerian Watch fluid pass by a point or an entire region Flow pattern Streamlines velocity is tangent to themk j i Vdt dt dt+ + =k j i V w v u + + =Flow Patterns Uniform flow0 =sV Non-uniform flow Steady flow Unsteady flow0 sV0 =tV0 tVLaminar vs Turbulent Flow Laminar TurbulentSystems Laws of Mechanics Written for systems System = arbitrary quantity of mass of fixed identity Fixed quantity of mass, m0 =dtdmdtm d ) ( VFrr=dtdWdtdQdtdE = Conservation of Mass Mass is conserved and does not change Momentum If surroundings exert force on system, mass will accelerate Energy If heat is added to system or work is done by system, energy will changeControl Volumes Fluid Mechanics Consider the behavior in a specific region or Control Volume Convert System approach Convert System approach to CV approach Look at specific regions, rather than specific masses Reynolds Transport Theorem Relates time derivative of system properties to rate of change of property in CV) (extensive energy momentum, mass, = = = CV CVd dm ) (intensive mass unit per of amount dmd== CV Inflow & OutflowArea vector always points outward from CVA Vr r = Qoutward from CV = = = CSin outA V A V Q QA VA V A Vr rr r r r1 1 2 21 1 2 2Reynolds Transport Theorem += +== + + + in outtt CV t t CVtt CV in out t t CVtt CV t ttsyst t

t t dtd0, ,0, ,0,0lim limlimlim + =+ = CSCVsysnetCVt tddtddtd

dtdt tA Vr r 0 0The time rate of increase of N within a system is equal to the time rate of increase of the property N within the control volume plus the netrate of efflux of N across the control volume boundary.Continuity Equation Reynolds Transport TheoremsysM=1 = = =dmdMdmdsysdm dm + =CSCVsysddtddtdA Vr r + =CSCV ddtdA Vr r 0 =CSA Vr r 0Unsteady Case Steady CaseBernoulli Equation Consider steady flow along streamline s is along streamline, and t is tangent to 11) (== + dsdVVgagzpdsdtand t is tangent to streamlineConstant2022222= + +=|||

\|+ +|||

\|=gVzpgVzpdsdgVdsdds ghead dynamic VelocitygVhead c Piezometri zp) (22== +gVzpgVzp2 222222111+ + = + + Energy Equation for Pipe Flowpump turbine shaftw w w =2 22222 1 112112 2u gzp Vu gzp Vw qshaft+ + + = + + + + 2 2) (2 21 2 22222 11211q u u w gzp Vw gzp Vturbine pump + + + + = + + +22222 112112 2zpgVh h h zpgVloss turbine pump+ + = + + +gq u uhgwhgwhlossturbineturbinepumppump = = =1 2; ;Momentum Equation Reynolds Transport Theorem + =CS CVsysddtddtdA Vr r = velocity; sys= system momentum= = FMrrd dsys sys = velocity; sys= system momentum + =CS CVddtdA V V V Fr r r r r = = FMrdtddtdsys sys Vector equation -- 3 components, e.g., x + =CS CVxu d udtdF A Vr r k j i Vr r r rw v u + + =Method of Analysis in Fluid MechanicsA. Theoretical Hydrodynamics Control volume & differential analysis Differential Fluid Element [free body diagram] Differential Equations Simplifying Assumptions Exact solutions only exist for simple geometry and conditionsTo arrive at a Prediction Equation:Eu = [ B, Fr, Re, Ma]24 Exact solutions only exist for simple geometry and conditions Approximate solutions for practical applicationsB. Experimental Hydraulics Similitude Dimensional Analysis Reduction Tools* Statistics* Numerical Analysis* GraphingApplications of EFM25Application in research & developmentTropic Wind Tunnel has the ability to create temperatures ranging from 0 to 165 degreesFahrenheit and simulate rainApplication in science & technologyPicture of Karman vortex sheddingApplications of EFM26Example of industrial applicationASA's cryogenic wind tunnel simulates flight conditions for scale models--a critical tool indesigning airplanes.Application in teachingFluid Mechanics laboratorySimilitude: Full and model scale27 Scales: model, and full-scale Selection of the model scale: governed by dimensional analysis and similarity